Diana, Sabrina and Opal had 1458 cards. Sabrina won some of the cards from Diana and as a result, Sabrina's cards increased by 50%. Opal then won some cards from Sabrina and Opal's cards increased by 80%. Finally, Opal lost some of her cards to Diana and Diana's cards increased by 20%. In the end, they realised that they each had an equal number of cards. How many percent less did Diana have in the end than what she had at first? Correct your answer to 1 decimal place.

Diana	Sabrina	Opal
1458
	2 u
- 1 u	+ 1 u
	3 u
		5 p
	- 4 p	+ 4 p
		9 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
80% = ⁸⁰₁₀₀ = ⁴₅
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 1458

1 group = 1458 ÷ 3 = 486

1 group = 6 boxes
6 boxes = 486

1 box = 486 ÷ 6 = 81

1 group + 1 box = 9 p
486 + 81 = 9 p
9 p = 567

1 p = 567 ÷ 9 = 63

4 p = 4 x 63 = 252

1 group + 4 p = 3 u
486 + 252 = 3 u
3 u = 738

1 u = 738 ÷ 3 = 246

Number of cards that Diana had at first
= 5 boxes + 1 u
= (5 x 81) + 246
= 405 + 246
= 651

Percent that Diana had less in the end than at first
= ^{651 - 486}₆₅₁ x 100%
≈ 25.3%

Answer(s): 25.3%